Automatic Extraction Method of Phenotypic Parameters for Phoebe zhennan Seedlings Based on 3D Point Cloud

Abstract

To address the inefficiency and significant errors in the manual measurement of phenotypic parameters of Phoebe zhennan seedlings, a non-destructive automated method based on a 3D point cloud was proposed for extracting phenotypic parameters of stem and leaves following stem and leaf segmentation. First, the processed point cloud image was aligned using the Sample Consensus Initial Aligment (SAC-IA) and Iterative Closest Point (ICP) algorithms to generate a three-dimensional model of the seedlings. The stem point cloud was extracted from the model using the median normalized growth vector-based search (MNVG) method, with the current growth vector refined based on previous growth points and vectors. These corrective processes enhanced the accuracy of stem extraction. The leaves were separated from the stem through streamlined projection, after which the remaining leaf point cloud was individually extracted using the density-based spatial clustering of applications with noise (DBSCAN) algorithm. The extracted stem data were used to measure stem length and stem diameter, and for each extracted leaf, leaf length, width, and area were measured, yielding accuracies of 97.7%, 93.2%, 96.4%, 88.02%, and 85.84%, respectively. The results of this study provide a valuable reference for forest breeding and the cultivation of high-quality tree seedlings.

1. Introduction

Phoebe zhennan, a rare timber species native to China, has been extensively utilized in high-end furniture, traditional architecture, and landscape design due to its fine grain, durability, and straight trunk [1]. However, its susceptibility to low temperatures restricts its cultivation to specific regions, including Sichuan, northwestern Guizhou, and western Hubei, thereby further exacerbating its scarcity. Given its significant market value and economic potential, artificial cultivation has been recognized as an effective approach to increasing its market availability and expanding its applications. Seedling development quality fundamentally determines the subsequent timber characteristics during silvicultural practices. The quantification of phenotypic parameters (e.g., stem length, diameter, leaf dimensions) during early growth stages is a critical methodology for growth monitoring. It provides essential morphometric data for growth prediction modeling, elite seedling selection, and precision nutrient management. Phenotypic measurement technology provides vital data support and technical assurance for research areas such as production management of Phoebe zhennan planting and seedling health assessment, utilizing quantification and precision. Thus, studying the phenotypic parameters of Phoebe zhennan seedlings is of significant practical value. Currently, the phenotypic measurement of Phoebe zhennan seedlings primarily relies on manual operations. However, manual methods are slow, inefficient, costly, and prone to significant error. Therefore, the fully automated phenotypic measurement of Phoebe zhennan seedlings has become an important research topic. Various imaging sensor platforms have been proposed for domestic and international plant seedling phenotype measurement. For instance, Li et al. [2] utilized an automated multi-view image acquisition platform to calculate stem and leaf phenotypic data using the Mask-RCNN network for the segmentation of point cloud images of cucumber seedlings. In contrast, Guan et al. [3] employed an RGB-based camera to capture two-dimensional images, followed by a structure-from-motion algorithm to generate a 3D point cloud for measuring phenotypic parameters such as plant height in Boehmeria nivea. Li et al. [4] used a monocular camera to capture data and applied a depth estimation network to obtain 3D depth information. Pekin B et al. [5] employed digital cover photography to measure the canopy cover and the leaf area index. Colaço A et al. [6] utilized a mobile terrestrial laser scanner and 3D modeling methods to obtain geometric data about orange trees. Ma et al. [7] measured the geometric information of apple trees in arid regions using hemispherical photography. This method determines apple trees’ canopy leaf area index in arid regions. Zhou et al. [8] used a time-of-flight (TOF) camera to develop a platform for measuring phenotypic parameters of Pinus massoniana. These reports demonstrate that stereo vision, structured light, and TOF have been applied to 3D phenotypic measurements of plants, directly extracting 3D information from images or depth data. Several studies have used the Microsoft Azure Kinect DK camera in portable acquisition settings to generate a spatial 3D point cloud of plants from color and depth images, leveraging perspective geometry. This device can fuse multi-sensor data, providing high-resolution, integrated platform references. In conclusion, this project integrates the technical literature on TOF imaging (Zhou et al. [8]) and the project’s requirements to develop a set of non-destructive 3D image acquisition devices tailored for Phoebe zhennan seedlings.

Research on 3D point cloud measurement methods in plants provides technical support for the phenotyping of Phoebe zhennan seedlings. The core step is the separation of stems and leaves to independently measure the phenotypic parameters of stems and leaves without interference between the organs. Point cloud organ segmentation methods commonly include traditional morphological processing algorithms and segmentation based on neural network architectures. The core of conventional morphological processing algorithms involves extracting local geometric structures and 3D shapes through processing and analyzing images (e.g., edge detection, contour extraction, morphological manipulation, etc.) based on the geometric features of different plant organs and their separation interfaces. Wang et al. [9] used the local eigenvalue of the point cloud to distinguish maize stem based on the stem’s strong linear shape and the leaves’ planar shape. This relationship represents the basis for distinguishing stems from leaves. Stein et al. [10] used the Locally Convex Connected Patches (LCCPs) method for clustering pepper plant leaves. Liu et al. [11] identified leaf point clouds using the 3D convex packet algorithm. Elnashef et al. [12] classified stem and leaf point clouds by computing different tensor features based on the local eigenvalue ratio relationship. These algorithms typically rely on the deep resolution of the plant structure. Neural network-based segmentation methods employ deep learning models, such as Convolutional Neural Networks (CNNs) and Generative Adversarial Networks (GANs) (Goodfellow et al. [13]), which learn features and structures of 3D phenotypes from large amounts of labeled training data (Li et al. [14]). Common network architectures include monocular deep estimation networks, PointNet and PointNet++ for point cloud processing [15,16,17], and 3D reconstruction networks such as PatchmatchNet (Wang et al. [18]). An upgraded version of this network, PointNeXt, has also been developed, enabling stem-and-leaf segmentation (Qian et al. [19]). These methods can automatically learn complex feature representations and establish mapping relationships, making them adaptable to handle complex and variable scenes. For Phoebe zhennan seedlings with known structural features, traditional morphological algorithms based on scheme design can meet segmentation requirements. In addition to the algorithms mentioned above, there are skeletonization algorithms such as L₁ median skeletonization (Huang et al. [20]), slice skeletonization (Xiang et al. [21]), and Laplace skeleton shrinkage (Wu et al. [22]), as well as local segmentation methods, such as region growing. A median normalized search (Jin et al. [23]) has also been applied, providing further references for this study. A comparison of these methods reveals that, due to the simple structure of Phoebe zhennan seedlings, skeletonization operations are unnecessary. Additionally, since direct clustering algorithms fail to separate stem and leaves, using search algorithms, such as median normalization, to first locate the stem and then cluster the leaves can improve measurement accuracy and reduce processing time.

An automatic system for measuring these parameters has been developed to solve the problem of fast and accurate measurement of phenotypic parameters of Phoebe zhennan seedlings. A set of stem and leaf separation algorithms has been proposed in this system. The initial stem point cloud is extracted using a median normalization search and corrected using the streamline projection method. Separate leaf and stem point clouds were obtained for measuring the respective parameters, including five phenotypic parameters: stem length, stem diameter, leaf length (Yang et al. [24]), leaf width, and leaf area (Hu et al. [25]) of the seedlings.

2. Materials and Methods

2.1. Data Objects and Acquisition Methods

Ninety-four Phoebe zhennan f. oblong seedlings from Shantou, Guangdong Province, China, were collected for this study, as the two-year cycle primarily constitutes the “nutrient growth” phase, characterized by the expansion of the root system, branches, and leaves. Upon completion of the two-year cycle, the seedlings enter the “reproductive growth” stage, which gradually enhances the lignification and structural stability of the tree. If the seedlings experience suboptimal growth during the first two years, subsequent growth may be hindered, potentially affecting the quality of the wood. Therefore, two-year-old Phoebe zhennan seedlings were selected as the subjects of this study. The seedling samples had heights ranging from 0.3 to 0.5 m, with crown diameters from 0.08 to 0.15 m, which capture most characteristics of the Phoebe zhennan seedling stage under two-year growth conditions, ensuring the adaptability of the algorithm to this stage.

The point cloud data acquisition platform was constructed using an Azure Kinect DK camera, a HUAVER11-125R axis micrometer fine-tuning slide, a black curtain, a Yunteng 691 stand, and a computer. Azure Kinect DK is capable of capturing and processing multi-dimensional data in real time due to its integrated RGB camera, depth sensor, IR sensor, and IMU. High-resolution depth perception and HD image capture, suitable for computer vision and various other fields, are supported. When combined with the powerful SDK and Azure cloud services, high-precision and low-latency real-time application development is supported. Additionally, its low cost makes it suitable for market adoption and practical applications. Therefore, this camera was selected as the experimental equipment. The specific parameters of the Azure Kinect DK camera include a resolution of 12 megapixels. When the working distance is less than 8.5 m, the measurement accuracy is approximately 2 mm. This group described the detailed construction process in the previous literature [8]. A matte steel background plate was added to this platform to reduce time-of-flight noise interference further and improve the quality of the acquired point cloud data. The point cloud data consist of n points in the format (x, y, z, r, g, b), where (x, y, z) represents the 3D spatial coordinates and (r, g, b) denotes the color information. These data are visualized as point cloud images using CloudCompare software[v2.12.4] [26]. The algorithm’s input and output include (x, y, z, r, g, b) point information, and its performance can be conveniently observed through these visualizations.

The Phoebe zhennan seedlings were placed on a fine-tuned sliding table, positioned 0.7 m from a matte background plate for point cloud data acquisition. In comparison, the camera was positioned on a triangular bracket, 1.2 m horizontally from the seedlings. The camera was angled at 25 degrees horizontally. The seedling was not moved for each image; however, the fine-tuning slide was rotated 180 degrees before capturing the subsequent image. A total of two point cloud images were taken at 0 and 180 degrees and later aligned to create a 3D model, optimizing the morphological representation of the Phoebe zhennan seedlings.

Data Validation

For parameter extraction validation, Phoebe zhennan seedlings were manually measured using specialized instruments, and the obtained values served as reference data. Stem length was measured using a flexible ruler from the point where the stem emerged from the soil to its apex. The stem diameter was measured using a Vernier caliper with an accuracy of 0.02 mm, 2 cm above the soil surface. Leaf length was determined by continuously measuring the leaf while rotating it 360 degrees and recording the maximum value. Leaf width was determined by measuring the maximum value perpendicular to the leaf length. The leaf area was calculated by scanning the leaves onto A4 paper using a scanner and computing the proportion of black pixel area relative to the total A4 paper area.

2.2. Research Methods

After data acquisition, each phenotypic parameter of the Phoebe zhennan seedling was obtained through data processing of the acquired point cloud images. As shown in Figure 1, the overall technical workflow facilitates the extraction of phenotypic parameters from the Phoebe zhennan seedling through four main steps: image preprocessing, point cloud alignment, stem and leaf segmentation, and parameter extraction. Image preprocessing: The background, flowerpot, and other non-plant parts were removed from the initial point cloud to obtain a pure Phoebe zhennan seedling point cloud. Point cloud alignment: The two point cloud images captured at 0 and 180 degrees were aligned to reconstruct a complete Phoebe zhennan seedling point cloud. SACIA (Sample Consensus Initial Alignment) was used for initial alignment, followed by ICP (Iterative Closest Point) for fine alignment to ensure high-precision alignment. Stem and leaf separation: The stem and leaf point clouds were separated to facilitate the independent measurement of phenotypic parameters. The median normalized growth vector-based search (MNVG) was applied to identify the stem structure, while DBSCAN (density-based spatial clustering of applications with noise) was employed for clustering leaves. For parameter measurement, the digital definitions of the phenotypic parameters in the point cloud were established to enable automatic calculation of stem length using Kruskal’s Minimum Spanning Tree. The stem diameter was measured using ellipse fitting. The leaf length and width were measured using Dijkstra’s algorithm. The leaf area was measured using the triangular gridded method. This structured approach ensures accurate and efficient extraction of phenotypic parameters from Phoebe zhennan seedlings.

2.2.1. Preprocessing

During the preprocessing step of each acquired initial point cloud image, factors unrelated to the research object, such as curtains and flowerpots, were removed, resulting in a simplified point cloud of the Phoebe zhennan seedling to facilitate subsequent processing. The group’s literature outlines the detailed algorithmic procedure for preprocessing [8]. Figure 2 is illustrated as follows: (a) a 2D color image of captured Phoebe zhennan seedlings and the background, (b) a 3D point cloud map, (c) a point cloud map after removing the curtain background, (d) a point cloud map following soil plane fitting and the removal of flower pots, (e) a point cloud map after time-of-flight noise removal, and (f) a pure Phoebe zhennan point cloud after the complete preprocessing.

2.2.2. Point Cloud Alignment

Point cloud alignment plays a critical role in phenotypic parameter measurement, ensuring the precise alignment of point cloud data from different viewpoints or time points, reducing measurement errors, and enhancing the accuracy of morphological parameters. Furthermore, alignment facilitates the integration of data from multiple perspectives into a complete 3D model, enabling comprehensive measurements of phenotypic parameters, such as plant height, canopy volume, and leaf area. Consistent alignment of point cloud data across different periods improves the accuracy of dynamic analysis, supporting the tracking of phenotypic changes during plant growth. By minimizing noise and systematic errors, alignment enhances the robustness of data processing and supports the development of automated analysis and high-throughput phenotyping studies.

Two preprocessed point cloud images of the same Phoebe zhennan object, captured at 0 and 180 degrees, were aligned to generate a complete 3D point cloud model of the seedling, as shown in Figure 2g. The alignment process involves a combination of SAC-IA coarse alignment and ICP fine alignment. To reduce computational complexity and improve the alignment algorithm’s efficiency, we applied voxel filtering to downsample all preprocessed point clouds before alignment, enhancing computational efficiency while preserving the morphological and structural features of Phoebe zhennan.

(1)

SAC-IA Coarse Alignment

The SAC-IA coarse alignment method involves calculating the Fast Point Feature Histogram (FPFH) for each point in the image to be aligned. Points with the closest feature descriptors in the source and target point clouds were identified as corresponding point pairs. A SAC-IA algorithm [27] was used to randomly select n sampling points from the source point cloud and extract their corresponding point pairs from the target point cloud. The transformation matrix was computed, and the matrix with the smallest root mean square error (RMSE) value was selected as the optimal transformation matrix, representing the coarsely aligned state.

(2)

ICP Fine Alignment

After the coarse alignment of the source and target point cloud data, the ICP algorithm [28] is applied to perform fine alignment, resulting in the aligned point cloud data. ICP fine alignment minimizes the distance between the source and target point clouds by iteratively updating the transformation matrix and recording the corresponding distances. Once the maximum number of iterations is reached, the transformation matrix associated with the smallest distance among all recorded distances is considered the optimal transformation matrix M. Three primary parameters are used in this process: the maximum number of iterations, the maximum matching distance, and the mean squared error. Increasing the number of iterations improves alignment accuracy but also increases computational time. Therefore, the number of iterations must be adjusted based on the complexity and accuracy requirements of the data.

2.2.3. Stem and Leaf Segmentation

The aligned 3D point cloud data (P_F) of Phoebe zhennan were used as input for the segmentation of stem and leaf point clouds, enabling the measurement and extraction of phenotypic parameters. This study employed the median normalized vector growth (MNVG) method for stem point cloud extraction, while the density-based clustering method was applied for leaf point cloud segmentation. The MNVG algorithm, an individual-oriented regional growth approach, segments the stem point cloud by performing a bottom–up search using median normalized vectors. The initial stem skeleton is obtained by iteratively identifying stem skeleton points, referred to as growth points, from the base of the stem.

This method is particularly effective for plants in which leaves are symmetrically distributed along both sides of the stem without overlapping. However, in Phoebe zhennan, leaves may emerge at multiple angles at the same height, and the neighboring region of a growth point may contain various leaf point cloud data, potentially misdirecting the growth vector of the next growth point toward the leaves, leading to errors in stem skeleton identification. Therefore, this study proposes a novel approach that utilizes the growth vector of an identified growth point to refine the directional computation of the subsequent growth point. Additionally, streamlined projection is applied to optimize the initial stem point cloud, followed by density-based clustering of the remaining leaf point cloud to achieve accurate stem and leaf segmentation. The detailed experimental procedure is outlined as follows.

Stem Extraction

Stem extraction consists of four primary steps: seed point identification, growth direction computation, growth point correction, and streamlined projection-based data optimization. The detailed steps are as follows:

(1)

Generation of the Seed Point s Using the L₁ Median Method

For accurate stem extraction, the initial search point must be positioned within the stem point cloud. Given the predefined orientation of the camera coordinate system, as obtained from DK camera imaging (as shown in Figure 3a), the captured data exhibit an inverted orientation in both the vertical and horizontal directions compared to the world coordinate system. The x-axis represents horizontal positioning, the y-axis denotes longitudinal positioning, and the z-axis corresponds to depth information. To enhance visualization and interpretation, we convert the data into the world coordinate system, as illustrated in Figure 3b. This transformation can be achieved using a transformation matrix T, whereby the entire dataset is rotated 180° clockwise around the z-axis. Multiplying the point cloud data by T yields the transformed point cloud data T′ in the world coordinate system.

Observations indicate that variations along the y-axis in the world coordinate system best represent the longitudinal structure of the input point cloud, facilitating the identification of the stem initiation point. Thus, the initial point is determined by identifying the coordinate y₁, corresponding to the minimum y_min value in the y-axis direction of the selected Phoebe zhennan point cloud. Subsequently, the point cloud set G is computed, including all points within the range of y_min + 2 cm. The median point of G is determined using the L₁ median algorithm and designated as the seed point s, represented as the blue point in Figure 3b. The L₁ median is the point in a multi-dimensional dataset that minimizes the sum of all L₂ (Euclidean) distances to the data points. The set G is subsequently incorporated into the initial stem dataset W. The specific procedure for determining the L₁ median seed point s is outlined below:

① Definition of point set G: Point set G consists of individual points g, each representing a coordinate in 3D space with an associated color value (x, y, z, r, g, b).

② Selection of the initial guess point: A random initial guess point s₀ is selected from point set G. Alternatively, the center point or the mean value of G may be used as the initial point.

③ Iterative computation of the optimal center point (L₁ Median): In each iteration, the Euclidean distance between the current guess point s₀ and all other points in G is computed as shown in Equation (1):

$$d(s_0,{\mathrm{g}}_i)=\sqrt{{(x_i-x_{s_0})}^2+{(y_i-y_{s_0})}^2+{(z_i-z_{s_0})}^2}$$

(1)

where (x_i, y_i, z_i) represents the coordinates of the guess point s₀ and $\left(x_{s_0},y_{s_0},z_{s_0}\right)$ denotes the coordinates of the remaining points in G.

The position of the guess point s is iteratively updated to minimize the sum of Euclidean distances between all points and the current guess point. The update process employs a weighted average or other optimization algorithms until the positional change in the guess point falls below a predefined threshold.

④ Termination condition: The iterative process terminates when the positional change in the guess point between two consecutive iterations falls below a predefined threshold. The final guess point s₀ is the L₁ median, representing the optimal seed point s.

(2)

Calculate the growth direction according to the seed point s

The seed point s growth direction is calculated in the spherical region with radius R, taking s as the center of the sphere. The points in the entire spherical region are represented by the set R(s), and the formula is expressed as in Equation (2):

$$R_{(s)}=\{\Vert (s,q){\Vert }_2<R,q\subset D\}$$

(2)

where $\left|\right|·\left|\right|$₂ represents the L₂ distance and the Euclidean distance, and the solution formula is shown in Equation (1). D represents all the point clouds of an individual Phoebe zhennan seeding, q is an arbitrary point in D, and R is the search radius calculated based on the Phoebe zhennan stem diameter. The search radius R is usually larger than that of the stem to prevent the omission of the stem point cloud, so the stem diameter is chosen as the value of R. The extracted seed point s stem diameter is used to calculate the search radius.

Calculating R involves calculating the first principal axis x₀ of the extracted point cloud collection G using Principal Component Analysis (PCA) and obtaining three slices of 0.002 m thickness by equidistant horizontal slicing along the first principal direction, with point y₁ as the starting point. The sliced data are then projected onto the seed, with point s as the origin, and the second principal direction slicing is performed with point s as the origin. Point s is the origin, and the second principal direction y₀ and third principal direction z₀ define the plane for ellipse fitting. The fitted ellipse is shown in Figure 3c,d, and the long axis of the three slices is taken as the mean value to determine the stem diameter, which is used as the search radius R.

Based on all points within R(s), the growth direction pointing to the next growth point is calculated from the median vector and density-based weights. All vectors are generated using the R(s) points as the endpoint and the seed point s as the start point. The vectors are then normalized by dividing by their respective modal lengths, ensuring each vector has the same weight when calculating the growth direction. As a result, the median vector of these normalized vectors tends to point in the direction centered at point s, where the inner points in R(s) are densely populated. For example, the points p₁, p₂, p₃, p₄, p₅, p₆ and p₇ shown in the left panel of Figure 3f below belong to R(s), where p₇ is a noise point. The vectors are obtained by subtracting the coordinates of the seed point s from the coordinates of each p-point, which are then normalized by dividing by their respective lengths. The endpoints of the final standardized vector are p′₁, p′₂, p′₃, p′₄, p′₅, p′₆, and p′₇, and they are put into the set D_p. The computation of the median standardized vector is based on the median value of the standardized vector, making it insensitive to the noise point p′₇, effectively avoiding its influence. The specific computation process of the growth vector is shown in Equation (3). Starting from the seed point s along the direction of the growth vector, the next growth point s′ can be found using the step size R. By continuously searching and updating the growth point s′, the initial skeleton point of the stem can be extracted. The calculation formula is shown in Equation (4):

$$\overrightarrow{m}=\mathrm{median}\{(P_p-P_s)/\Vert P_p-P_s{\Vert }_2,P_p\in D_p\}$$

(3)

$$s^{\prime }=s+R\times \overrightarrow{m}$$

(4)

where P_p represents the 3D coordinates (x, y, z) of point p, p is a set of all points within R(s), and P_s represents the 3D coordinates (x₁, y₁, z₁) of the current seed point s. ${\left|\right|·\left|\right|}_2$ represents the L₂ distance, and R is the search radius of the step size. s′ represents the coordinates of the next growing point and $\overrightarrow{m}$ is the growth direction vector. D_p is the set of vector endpoints normalized concerning all points within R(s).

Note that because the bottom 2 cm of the stem is intercepted to calculate the starting point s, the search radius of the first growth point should be configured to the search radius R plus 1 cm to prevent R(s) from being empty, which would result in the inability to calculate the next growth direction vector, thus halting the growth. Meanwhile, to ensure that the growth direction is always upward along the stem, the data in R(s) corresponding to each newly obtained growth point are no longer included in the entire plant point cloud set D used to calculate the R(s) for the next growth point. They are added to the initial stem point cloud set W each time R(s) is updated.

To further describe the growth process from below, ${\overrightarrow{m}}_0$ is defined as an initial growth vector, with the starting point of the vector being the seed point s, and the endpoint of the vector ${\overrightarrow{m}}_0$ being the first growth point s′ found. The growth vector corresponding to the growth point ${\overrightarrow{m}}_t$ above can be obtained by continuously searching upward, where t represents the vector order number, and the number of times it grows upward is t − 1.

(3)

Growth point correction as well as growth cessation.

When a small number of incompletely removed noise points or multiple unevenly distributed leaves, with heights similar to the connection point of the stem, exist, the data within R(s) corresponding to the growth point s′ may contain both the stem data and the point cloud data of multiple leaves. At this point, a single search through median growth may direct the growth vector toward the leaves, leading to an error in stem extraction, as shown in Figure 3e. A correction scheme based on median growth has been proposed to address this issue. Specifically, the growth vector of the previous growth point is used for correction, as shown on the right-hand side of Figure 3g above, and the formula is provided in Equation (5) below:

$$\overrightarrow{v}=\{({\overrightarrow{m}}_{t+1}+{\overrightarrow{m}}_t)/\Vert {\overrightarrow{m}}_{t+1}+{\overrightarrow{m}}_t{\Vert }_2,t\ge 1\}$$

(5)

$${\overrightarrow{m}}_{t+1}=\overrightarrow{v}$$

(6)

where $\left|\right|·\left|\right|$₂ denotes the L₂ distance. $\overrightarrow{v}$ represents the transient vector, and ${\overrightarrow{m}}_{t+1}$ corresponds to the corrected growth vector for the t + 1 growth iteration. This vector is reassigned to update ${\overrightarrow{m}}_{t+1}$, finalizing the correction of the growth vector. If t + 1 indicates the ordinal number of the current growth vector, then t represents the ordinal number of the previous vector. When t = 0, it signifies the initial growth vector, which does not require correction as no preceding vector exists.

The correction process is optimized by incorporating the corrected growth vectors from n(n > 1) previously identified growth points. The corrected search condition is illustrated in Figure 3g, with the correction formula expressed in Equation (7):

$${\overrightarrow{m}}_{t+1}={\displaystyle \frac{1}{n}}({\overrightarrow{m}}_{t+1}+{\overrightarrow{m}}_t+{\overrightarrow{m}}_{t-1}+\dots +{\overrightarrow{m}}_{t+1-n})$$

(7)

where ${\overrightarrow{m}}_{t+1}$ denotes the growth vector directed toward the next growth point, while ${\overrightarrow{m}}_t$ indicates the growth vector at the current growth point. Here, t signifies the growth iteration number, and n represents the count of corrected growth vectors employed.

Once the new growth point is identified, R(s) is updated according to Equation (1). The updated R(s) is then compared to the previous R(s). Suppose no additional point cloud data are incorporated into R(s). This indicates that the stem apex has been reached, thereby terminating the growth process. R(s) can be conceptualized as a sphere that expands continuously from the base upward, forming a representation of the stem. If no new point cloud data are added within R(s), the initial stem point cloud set W is generated, as illustrated in Figure 4a.

(4)

Streaming projection optimized stem data.

Since the search step R corresponds to the stem diameter, W inevitably includes a portion of the leaf point cloud data. Further refinement is required to optimize the extracted stem point cloud data W while preserving the true dimensions of the leaf data as accurately as possible. The initial stem point cloud W, extracted using the median normalization algorithm, can be refined using the streamline projection method to obtain a modified stem point cloud skeleton. The corrected point cloud skeleton is then used to extract the stem point cloud data through the neighborhood point search approach, effectively separating the stem point cloud obtained via median normalization from the leaf point cloud. The detailed steps of the streamlined projection process are outlined as follows:

A.

Determining the stem coordinate system

The initial stem point cloud W, identified through the median normalization search, is analyzed using PCA to determine the three principal directions. The coordinate system is then established with the center of mass of the initial stem data as the origin and the three principal directions as its axes, as illustrated in Figure 4b. The first principal direction is defined as the x′-axis, the second as the y′-axis, and the third as the z′-axis.

B.

Two-dimensional plane projection

Three planes were obtained by forming a plane between two of the established coordinate axes, and the initial stem point cloud datum W was projected onto the three planes, respectively, to obtain three 2D projection data. The two-dimensional optimal planar skeleton fitting was performed on the three projection data, as shown in Figure 4c–h. The curve fitting was solved using the least squares fitting of a binary H-th degree polynomial, as shown in Equation (8) below. The coefficient matrix was constructed from the resulting polynomial, and the coefficients were solved using Singular Value Decomposition (SVD).

$$p(x)=w_0+w_{1}x+w_2{x}^2+\dots +w_H{x}^H$$

(8)

where w₀, w₁… w_H are the coefficients of the equation; H is the order of the equation, which is configured to the seventh order in this paper; x is the x-value of the projection data, and p(x) is the y-value of the projection data.

C.

Finding the best projection plane

The coordinates of the points in the initial stem point cloud W are substituted into the following polynomial fitting Equation (8) in three-dimensional space to solve for the coefficients of the equation. The x and y coordinates of all points on the three projection planes from Step B are then substituted into the equation, and the corresponding z-coordinates are computed, reducing the two-dimensional projection data into three-dimensional space. Equation (9) is a polynomial fitting model in three-dimensional space that characterizes the nonlinear relationship between x, y, and z for a specific point after fitting. The reduced 3D points from the three projection planes and the initial stem point cloud W are indexed to identify the corresponding points. The L₂ distance calculates the error and Min(E) of the corresponding points. The calculation process is shown in Equation (10). The projection planes corresponding to the error and Min in the three reduced datasets are identified as the best projection planes (one of the three planes in Step B is the optimal surface).

$$\begin{array}{l}z=a_0{x}^3{y}^3+a_1{x}^3{y}^2+a_2{x}^3{y}^1+a_3{x}^2{y}^3\\ +a_4{x}^2{y}^2+a_5{x}^2{y}^1+a_6{x}^0{y}^3+a_7{x}^0{y}^2\\ +a_8{x}^0{y}^1+b\end{array}$$

(9)

where a₀, a₁, a₂, a₃, a₄, a₅, a₆, a₇ and a₈ are the coefficients of the equations, x and y are the two-dimensional coordinates x-value and y-value of the projection point, and b is a constant term. z represents the three-dimensional z-value coordinates of the reduction.

$$\mathrm{Min}(E)=\left\{{\displaystyle \sum {‖P_{(x,y,z)}-P_{md(x_2,y_2,z_2)}‖}_2},d=1,2,3\right\}$$

(10)

where $P_{md(x_2,y_2,z_2)}$ are the reduced 3D coordinates. d = 1, 2, 3 corresponds to the data reduced for each of the three projection surfaces. $P_{(x,y,z)}$ represents the input Phoebe zhennan 3D model data.

D.

Modified three-dimensional skeleton point calculation and modified stem extraction

Step A shows that the optimal projection plane involves two main directions. Points on the plane in these two directions align with the direction of the largest coordinate difference. The maximum and minimum values of the coordinates are calculated for the direction of the maximum axis, and the difference is divided by N − 1. This results in N evenly spaced points, incrementing the final step by one from the minimum value along the maximum axis. The coordinate values are substituted into the curve equation obtained from Equation (6), which provides the coordinate values of the N points in the other direction on the optimal projection plane. The corresponding points in the two-dimensional coordinate system represent the skeleton points. These two-dimensional coordinates are then substituted into Equation (8) to obtain the optimal three-dimensional skeleton points, as shown in Figure 5a. The optimized stem point cloud data point W_Y is obtained by searching all the 3D skeleton points through neighborhood points, using R/2 as the radius, as shown in Figure 5b.

Leaf Extraction

The point cloud of the Phoebe zhennan seedling is subtracted from the stem point cloud W_Y extracted in the previous step to obtain the set of all leaf point clouds. Individual leaves are segmented using the density clustering method DBSCAN. In the DBSCAN algorithm, the neighborhood radius and the minimum number of points required are two important parameters. The neighborhood radius defines the extent of the point’s neighborhood in the leaf clustering process, while the minimum number of points required determines whether a point is a core point. A core point helps the algorithm identify and extend the region where density is reachable, forming clusters for the segmentation of individual leaves. The neighborhood radius is set based on the distribution density and range of the data points. If the radius is too large, different clusters that should not be merged may be incorrectly combined; if it is too small, too many noise points may result, preventing proper cluster formation. The results, shown in Figure 5c, illustrate optimal clustering segmentation, with each individual clustered leaf represented by a different color.

2.2.4. Parameter Measurement

Stem Length and Stem Diameter

The stem of the Phoebe zhennan seeding tends to grow vertically during the seedling stage. Based on this feature, the extracted stem data were searched using vector-corrected median normalization, and the skeleton points were extracted through streaming projection. The three-dimensional skeleton points were connected using the Kruskal Minimum Spanning Tree (MST), and the lengths of all edges in the MST were summed to obtain the stem length, as defined in Equation (11):

$$Ds={\displaystyle \sum _{(i,j)\in MST}\sqrt{{(x_i-x_j)}^2+{(y_i-y_j)}^2+{(z_i-z_j)}^2} }$$

(11)

where $(x_i ,y_i ,z_i )$ and $(x_j ,y_j,z_j )$ denote the three-dimensional coordinates of two adjacent points in the MST.

The stem diameter was calculated by fitting the major axis of the ellipse to the point cloud slice data G at the bottom end of the stem in the projection plane. The general quadratic equation for ellipse fitting is shown in Equation (12):

$$A{x}^2+Bxy+C{y}^2+Dx+Ey+F=0$$

(12)

where A, B, C, D, E and F are fitting coefficients obtained using the least squares method. The center of the ellipse (h, k) is calculated as shown in Equation (13):

$$h={\displaystyle \frac{BE-2CD}{4AC-B^2}} ,k={\displaystyle \frac{BD-2AE}{4AC-B^2}}$$

(13)

The rotation angle θ, which determines the orientation of the ellipse, is calculated as shown in Equation (14):

$$\theta ={\displaystyle \frac{1}{2}} arctan({\displaystyle \frac{B}{A-C}} )$$

(14)

After transforming the coordinate system so that the ellipse center is at the origin and rotating it by θ, the standard ellipse equation is calculated as shown in Equation (15):

$${\displaystyle \frac{{(x^{\prime }cos\theta +y^{\prime }sin\theta )}^2 }{a^2}}+{\displaystyle \frac{{(-x^{\prime }sin\theta +y^{\prime }cos\theta )}^2}{b^2}} =1$$

(15)

where $x^{\prime }=x-h$ and $y^{\prime }=y-k$ represent the transformed coordinates. Finally, the stem diameter D was calculated as shown in Equation (16):

$$D=2a$$

(16)

where a is the major semi-axis of the fitted ellipse.

Leaf Length and Leaf Width

For the segmented leaf data, alignment errors may cause the leaf surface points in the point cloud to exhibit a concave–convex distribution. Manual measurement of the actual leaf area requires the scanner to flatten the leaf during scanning, which causes the leaf to approximate a smooth plane. Therefore, smoothing the segmented leaf point cloud can improve the accuracy of the leaf area. The moving least squares (MLSs) method smooths the point cloud. The order of the plane fitting equation is configured to second order, and the neighborhood search range is 0.01 m. The result is shown in Figure 6c.

Based on the literature review on the morphology of Phoebe zhennan leaves, the two points with the farthest Euclidean distance in the leaf point cloud are defined as the leaf base point P and the leaf tip point Q, as shown by the blue and yellow points in Figure 6a. The two points in the leaf, passing through the main leaf vein (also known as the midvein), are connected as shown by the red circle and white line segments in Figure 6a. The path tends to follow straight line segments. The length of the midvein can be approximated to determine the length of the leaf. Using the leaf base point P and the leaf tip point Q, the Dijkstra algorithm is applied to approximate the path of the midvein in the leaf point cloud. The core principle is to start from the source point, gradually selecting the closest untraversed vertices from the source point and updating the length of neighboring vertices along the path until the shortest path is found from the source to all other vertices in the graph. The algorithm ensures that a locally optimal path decision is made at each step by continuously optimizing the distance estimates of the vertices to be processed. Since the shortest path search is conducted through the known points P and Q, it can be set as the starting point or endpoint without affecting the search for the shortest path. For consistency in this paper, point P is set as the starting point, and point Q is set as the endpoint.

The initial midvein path is found using Dijkstra’s algorithm, as shown by the dark blue point in Figure 6e. To improve the fitting results of the midvein, the optimal plane S_leaf is calculated by randomly sampling the fitting planes for a single leaf point cloud (Figure 6d). Then, the S_vein plane, passing through points P and Q and perpendicular to the S_leaf is calculated. The point cloud data of the initial leaf midvein is projected onto the S_vein plane to obtain the corrected leaf midvein point cloud path, as shown by the light blue point in Figure 6e. The distances between each point and its neighboring points in the point cloud of the modified midvein path are calculated and accumulated to approximate the leaf length.

The leaf length is calculated as in Equation (17):

$$Dk={\displaystyle \sum _{(i,j)\in Dijkstra}\sqrt{{(x_i-x_j)}^2+{(y_i-y_j)}^2+{(z_i-z_j)}^2} }$$

(17)

where i, j are the indices of two adjacent points on the Dijkstra path, $(x_i ,y_i ,z_i )$ and $(x_j ,y_j,z_j )$ are their 3D coordinates, and Dk represents the total leaf length.

After determining the leaf length, the leaf width can be calculated by first projecting all leaf points onto the leaf vein projection plane. The Euclidean distances from each projection point to the original point are then compared, and the point with the largest distance is selected as the starting point for the leaf width, as indicated by the yellow point in Figure 6e. A search is then conducted to find the point on the leaf vein path with the closest Euclidean distance to the yellow point. The initial shortest path between the two yellow points is then calculated, and the purple point is added to the original point. The initial shortest purple path, corrected similarly to the leaf length, is used to calculate half of the leaf width, as shown in Figure 6e. Since Zhennan leaves are symmetric, the computed value is multiplied by two to obtain the leaf width.

Leaf Area

The leaf area was calculated using a triangular sectioning algorithm to construct a point cloud mesh for a single leaf. The areas of all the triangles were then summed to obtain the total leaf area. As shown in Figure 6f, the area of each triangle was calculated using Heron’s formula, and the leaf area was approximated by summing the areas of all triangular facets. The computational workflow consists of three main steps:

(1)

Surface mesh generation: The greedy-projection triangulation algorithm was employed to project the 3D point cloud onto a 2D plane, generating a Delaunay triangular mesh while preserving its topology. The point cloud was then projected onto the best-fit plane, which was determined using PCA. A Delaunay triangular mesh was subsequently constructed on the projection plane and then mapped back to 3D space, forming the leaf surface mesh.

(2)

Local area calculation: The area of the leaf’s triangular mesh was calculated using Heron’s formula for triangle area calculation, as shown in Equation (18):

$$A=\sqrt{s(s-a\left)\right(s-b\left)\right(s-c)}$$

(18)

where a, b, c denote the lengths of the three sides of the triangle, and s represents its semi-perimeter.

(3)

Total area integration: The total surface area of the leaf was obtained by iterating through all triangular facets, computing their areas, and summing them together.

When triangular meshing the leaf, using a larger side length results in larger triangle areas, which reduces the number of triangles in the model. This, in turn, leads to a loss of detail, particularly in the curves and fine features, reducing the accuracy of the final area calculation. In order to improve area accuracy, a smaller edge length threshold is applied. However, this may result in points in the leaf point cloud being too far apart to connect into a triangular mesh, leading to holes. Thus, a hole repair algorithm is required.

The hole repair algorithm consists of two steps: search and repair. Examining the characteristics of the hole boundaries can determine if they correspond to the edge of the hole. If the edge corresponds to only one triangular surface piece, it is identified as the hole’s edge. All hole points and edges are extracted, as shown in Figure 6g. The edges of the leaf’s triangular face pieces correspond to only one triangular face piece, but these edges are not hole edges. To identify the unwanted leaf edge, all hole edges forming rings are searched, and the ring with the most points is selected. This can then be deleted to reveal all holes that require repair, as shown in Figure 6h. Holes with only three points are repaired by adding the three points directly as the vertices of a triangle into the triangular mesh. For polygonal holes, a random point is selected as the starting point from the extracted hole, and two consecutive neighboring points are used as the three vertices of the triangle until the starting point is connected to all points in the hole. The areas of all these triangles are then summed to complete the hole repair. The final patched and perfected triangular meshing is shown in Figure 6i. By following the method described above, the sum of the triangular mesh area and the internal hole area of a single leaf are calculated to determine the size of a single leaf area, and the result is divided by two as the estimation of the leaf area of that leaf, considering the front and back sides.

To verify the accuracy of the area calculation, each leaf was scanned onto A4 paper using a scanner. The scanner was binarized to calculate the proportionate area of the black pixels on the A4 paper, which was then scaled up to indirectly obtain the leaf’s actual area.

3. Analysis of Experimental Results

3.1. Preprocessing Results

To verify the reliability and validity of the image preprocessing, the stem length, stem diameter, leaf length, leaf width, and leaf area of 20 Phoebe zhennan seedling samples were manually measured using the validation method described in Section 2.2.2. The validation dataset included data for 20 stems and 126 leaves. Experimentally, the stem length of the manually cut plants from the same point cloud image and the stem length obtained from segmentation using the preprocessing algorithm was measured by CloudCompare with an accuracy of 98.9%. The average accuracy of the stem diameter was 98.6%, the leaf length was 97.9%, the leaf width was 98.6%, and the leaf area was 98.3%. These results demonstrate that the preprocessing algorithm applies to Phoebe zhennan seedlings.

3.2. Alignment Results

The voxel radius side length was configured to 0.006 m. During the alignment stage, several experiments found that setting the n value to 6 resulted in higher alignment accuracy and effectively improved alignment speed. A total of 5000 ICP iterations were configured for fine alignment in order to meet the specified requirements. Setting a larger matching distance value increases the likelihood of finding a matching point but may result in inaccurate matches. A smaller value improves matching accuracy but may result in some points not being matched. Therefore, a balanced value of 0.05 m was selected for this project. The RMSE of corresponding point pairs was adopted as the convergence criterion for the control algorithm. A smaller threshold improves alignment accuracy but results in a higher number of iterations and increased computational cost. Based on extensive experimental evaluations, the RMSE thresholds were configured to 0.003 m for coarse alignment and 0.001 m for fine alignment. Once the RMSE drops below the corresponding threshold following matrix transformation, the iterative process is terminated and the optimal transformation matrix is produced.

The aligned point cloud data of the plants were utilized to measure stem length, stem diameter, leaf length, leaf width, and leaf area, in order to verify the feasibility of the proposed method, following the procedure described in Section 2.2. These measurements were subsequently compared with ground truth values obtained through manual measurements. The same 20 Phoebe zhennan seedlings, including 20 stem samples and 126 leaf samples, were used to assess alignment accuracy. The average accuracies achieved were 98.1% for stem length, 97.6% for stem diameter, 97.5% for leaf length, 95.6% for leaf width, and 93.3% for leaf area. All results showed accuracy errors of less than 10%. These findings demonstrate the applicability of the alignment algorithm to Phoebe zhennan seedlings.

3.3. Stem and Leaf Segmentation Results

The alignment 3D point cloud data were subjected to stem–leaf segmentation. A median-normalized growth vector method was used for stem detection, with the number of correction points configured to 1, 2, 3, and 4 to conduct search experiments on 20 plant samples. The point cloud segmented by this algorithm is analyzed with the corresponding manually segmented point cloud, and the percentage of overlapping points is obtained to become the segmentation accuracy, and the average segmentation accuracy is calculated as a reference for the selection of the optimal value of the parameter after experimenting with the data of 20 sample plants. This evaluation method was simultaneously applied to the effect evaluation of the subsequent three parameters.

During the streamlined projection correction process, the number of skeleton points after the correction was identified as a key factor in accurately and uniformly representing the morphology of the Phoebe zhennan seeding stem. For independent leaf clustering following stem extraction, multiple DBSCAN clustering experiments were conducted with varying search radii and minimum point counts to ensure optimal clustering performance.

Based on the experimental procedure and results, a parameter sensitivity analysis (PSA) was performed on four parameters to illustrate the process better. For each parameter, multiple values were selected based on experimental experience, and the corresponding results were compared to determine the optimal value. Experimental effectiveness was evaluated by comparing the number of detected points to those obtained from manual segmentation.

Based on laboratory experience, four key parameters were selected for analysis: the number of corrected growth points, the number of skeleton points, the DBSCAN search radius, and the minimum number of DBSCAN clustering points. The number of corrected growth points varied from 1 to 4 in step 1; the number of skeleton points varied from 30 to 70 in step 10. The DBSCAN search radius ranged from 0.002 m to 0.0065 m, in increments of 0.0015 m, and the minimum number of DBSCAN clustering points ranged from 3 to 6, in steps of 1.

Considering the interdependence among parameters, experiments on each parameter were conducted while fixing the others at their respective optimal values. Multiple experimental results were obtained and analyzed to determine the optimal values for the four parameters, as presented in

Table 1. Sensitivity analysis of key parameters in point cloud segmentation.

Parameter Name	Value	Average Segmentation Accuracy of Stem Point Cloud	Optimal Value
Number of corrected growth points	1	55.3%	3
	2	80.1%
	3	95.6%
	4	85.4%
Number of Skeleton Points	30	28.2%	50
	40	83.3%
	50	98.23%
	60	86.2%
	70	67.8%
DBSCAN Searching Radius (m)	0.002	73.5%	0.0035
	0.0035	96.9%
	0.005	89.2%
	0.0065	63.7%
DBSCAN Searching Minimum Points	3	93.4%	5
	4	93.9%
	5	95.24%
	6	92.4%

.

The highest segmentation effectiveness (95.6%) was achieved when the number of corrected growth points was configured to three. However, when the number of corrected points deviated from this value, segmentation effectiveness decreased significantly by 10% to 40%, indicating a threshold effect that identifies three as the optimal value. Regarding the number of skeleton points, it was confirmed through experimentation that an appropriate number ensures morphological accuracy. Within the interval of 40, 50, and 60 skeleton points, segmentation efficiency fluctuated by less than 3%, indicating minimal variation in performance. Within this range, fifty skeleton points yielded the best experimental results.

Additionally, it was observed that the optimal segmentation performance for leaf detection using DBSCAN was achieved with a search radius of 0.0035 m and a minimum of five clustering points, effectively circumventing the influence of noise. Based on the above experimental results, the optimal parameters were determined as follows: three correction points, fifty skeleton points, a DBSCAN search radius of 0.0035 m, and a minimum of five clustering points. These settings achieved the optimal balance between efficiency and accuracy, further demonstrating the robustness and scientific validity of the proposed method.

Figure 7 shows the schematic diagram of the stem and leaf segmentation effect for six Phoebe zhennan seedlings using the method described in this paper. The black color represents the stem point cloud, while other colors denote the separate leaf point clouds.

3.4. Comparison of the Results of Different Stem and Leaf Segmentation Methods

The stem and leaf segmentation directly affect the completeness and accuracy of parameter measurement. Therefore, the effectiveness of the segmentation method proposed in this paper was verified by comparing it with multiple other segmentation methods. First, the true values of the stem and leaf segmentation method were manually measured using CloudCompare software to sort the leaf and stem point clouds of the 20 aligned Phoebe zhennan seedlings from the previous steps. The stem point cloud was marked 0, and the leaf point cloud was marked 1. The number of stem point clouds and leaf point clouds were then statistically counted as the true values. Different segmentation algorithms were applied to the same 20 Phoebe zhennan point cloud datasets. The segmentation results were used as the test values, including points attributed to the stem point cloud or the point cloud of a single leaf. The stem and leaf segmentation results obtained using the algorithm proposed in this paper were compared with the tensor-based segmentation method of Elnashef et al. [12] and the slice-based skeleton method of Xiang et al. [21]. In order to more comprehensively evaluate the segmentation performance of stems and leaves, the Matthews correlation coefficient (MCC) was employed as the evaluation metric. Compared to traditional accuracy, MCC takes into account true positives (TPs), false positives (FPs), true negatives (TNs), and false negatives (FNs), making it more suitable for datasets with class imbalance. Furthermore, the Pearson correlation of MCC values was calculated across different methods to analyze their impact on segmentation accuracy. The calculation formula is shown in Equation (19):

$$MCC={\displaystyle \frac{TP\times TN-FP\times FN}{\sqrt{(TP+FP)(TP+FN)(TN+FP)(TN+FN)}}}$$

(19)

where TP represents the point cloud of correctly classified leaves, TN represents the point cloud of correctly classified stems, FP represents the point cloud of misclassified leaves, and FN represents the point cloud of misclassified stems. The specific segmentation results are shown in

Table 2. Comparison of segmentation results of different methods for data from 20 identical Phoebe zhennan seeding.

Methodologies	Average Segmentation Accuracy of Stem Point Cloud	Average Segmentation Accuracy of Leaf Point Cloud	Average Segmentation Speed (ms/plant)	MCC (Correlation Coefficient)
Tensor-based segmentation + DBSCAN	96.52%	90.65%	9094	0.78
Segmentation skeleton based + DBSCAN	94.85%	95.43%	13,435	0.80
Our method	98.23%	95.24%	7547	0.88

.

The segmentation results of PointNet++ (Qi et al., 2017 [17]) and the PointNeXt method (Qian et al., 2022 [19]) were used for comparison, with the detailed segmentation results presented in

Table 3. Comparison of segmentation results of deep learning methods for 20 identical Phoebe zhennan seeding.

Methodologies	Average Segmentation Accuracy of Stem Point Cloud	Average Segmentation Accuracy of Leaf Point Cloud	Average Segmentation Speed (ms/plant)	MCC (Correlation Coefficient)
(PointNet++) + DBSCAN	92.42%	93.88%	11,452	0.83
PointNeXt + DBSCAN	89.31%	91.73%	8624	0.80
Our method	98.23%	95.24%	7547	0.88

. The 94 heather samples obtained from the experiment were augmented to generate 500 plant data points, which were divided into 400 samples for the training set, 100 for the validation set, and 20, consistent with the traditional method, for the test set. The specific segmentation results are shown in Table 3.

The information in Table 2 reveals that both tensor-based segmentation and slice skeleton-based segmentation are inferior to the method proposed in this paper. When the multi-order tensor-based method is used to classify the 3D point cloud into plant organ levels, parameter settings, particularly the selection of the search radius, are crucial for choosing neighboring points and calculating tensor features. Improper parameter settings may fail to capture the plant’s structural features correctly. Furthermore, the geometric complexity of Phoebe zhennan, including morphological diversity and organ crossover, increases the difficulty of classification. Although the number of segmented leaves is the same, some points are missing in each leaf. This is shown in Figure 8, where the blue points represent the identified stem point cloud, and the green points represent the identified leaf point cloud. This can lead to significant errors in subsequent leaf area calculations. When using the slice skeletonization method for classification, the center of mass of each slice is calculated as the skeleton point. The Hough transform detects the centerline of the stem, and points adjacent to the centerline are extracted as stem skeleton points using a thresholding strategy. This method has significant limitations, though it produces better results for crops with stems that tend to grow vertically. However, it may lead to the omission or even failure to extract stem points when the Phoebe zhennan seedling exhibits significant stem bending.

Table 3 shows that PointNet++ is a deep learning approach based on local feature extraction, capable of effectively capturing local structural information in point clouds and exhibiting notable advantages in segmentation accuracy. However, this method involves high computational complexity and a large model architecture, resulting in relatively slow processing speeds and difficulty meeting the requirements of efficient real-time applications. PointNeXt, by contrast, is a modular network architecture designed for large-scale point cloud data, offering strong feature modeling capabilities and being particularly well-suited for handling massive point cloud datasets. However, its performance tends to be unstable in small-sample scenarios and is highly dependent on the quality and diversity of labeled training data. In addition, both methods require large-scale, high-quality, manually annotated training datasets.

In summary, the segmentation scheme proposed in this study is more efficient than the other four methods in both stem and leaf segmentation tasks. It requires less processing time and achieves higher segmentation accuracy compared to the other methods.

3.5. Measured Parameter Results and Error Analysis

In this study, the existing data of 94 Phoebe zhennan seedings were processed, resulting in the segmentation of 94 stems and 630 leaves. After extracting the parameters, linear regression analysis was performed between manual and system-derived measurements for all extracted parameters. The correlation coefficient (r), coefficient of determination (R²), mean absolute error (MAE), and root mean square error (RMSE) were calculated for four parameter indices to assess the effect. The relationship between the correlation coefficients of each parameter was visualized using a linear plot, as shown in Figure 9. The results of the measurement calculations are presented in

Table 4. Parameterized list of indicators.

Measurement Indicators	Correlation Coefficient (r)	Coefficient of Determination (R2)	Mean Absolute Error (MAE)	Root Mean Square Error (RMSE)
Stem length	0.9773	0.9551	0.8921 cm	1.1416 cm
Stem diameter	0.9319	0.8684	0.3808 mm	0.4551 mm
leaf length	0.9641	0.9295	0.3659 cm	0.5258 cm
Leaf width	0.8802	0.7748	0.2674 cm	0.3573 cm
Leaf area	0.8584	0.8584	2.6836 cm2	3.3983 cm2

.

Errors in the analysis of stem length, stem diameter, leaf length, leaf width, and leaf area are attributed to the incomplete removal of flight noise from the device and errors caused by the improper removal of edge point clouds during the denoising process. Additionally, ensuring the complete separation of the stem and leaf at the stem-leaf junction is difficult, which may result in the presence of part of the stem point cloud in the leaf, leading to errors in the leaf parameters. The stem length error results from deviations between the fitted skeleton equations and the actual skeleton during the optimization of the initial stem point cloud, leading to errors in the final stem length. The stem diameter error occurs during point cloud alignment due to the large number of leaf point clouds. As the number of feature points increases, the alignment matrix weights favor the leaves, causing errors in stem alignment. This, in turn, leads to errors in parameter extraction during ellipse fitting. The leaf length error arises from the growth characteristics of Phoebe zhennan seedlings, where the stem diameter decreases from the root to the tip. When neighborhood points are extracted from the corrected stem skeleton using the base radius of the stem, part of the top leaf point cloud may be mistakenly extracted into the stem point cloud, leading to errors in leaf length and leaf area parameters. The leaf length error and the lack of complete symmetry in the leaf influence the leaf width error. While leaf width can be calculated simultaneously on both sides, the accuracy improvement is limited, and the increased computational load reduces the algorithm’s efficiency.

Overall, the measured phenotypic parameters are either higher or lower than the actual values. However, the correlation coefficients and other indices meet the application requirements, indicating that this program is highly reliable and applicable for extracting phenotypic parameters from Phoebe zhennan seedlings.

4. Discussion

The phenotyping system proposed in this study is suitable for the automated measurement of key phenotypic parameters—such as stem length, stem diameter, leaf length, leaf width, and leaf area—for Phoebe zhennan seedlings with heights of up to 1.5 m. In general, the height of Phoebe zhennan seedlings does not exceed 1.5 m from the time of container transplanting through approximately two years of growth, thereby allowing the system to cover the entire nursery stage effectively. The experimental samples used in this study were primarily within the 0.3–0.5 m range, corresponding to the main indoor nursery stage. As the plants grow taller, the system and its supporting algorithms can be adapted to later growth stages by adjusting the imaging distance and preprocessing parameters—such as those related to pass-through filtering—without modifying the core algorithms. The experimental results demonstrate high stability and reliability under controlled conditions, indicating strong potential for future deployment in complex field environments.

In terms of application scenarios, the current system is designed for the independent imaging of individual containerized seedlings, offering low interference and high segmentation accuracy. This characteristic provides broad potential for deployment across multiple application domains, such as seedling screening in scientific research institutions, nursery-stage growth monitoring in forestry farms, digital forest farm management, and other Phoebe zhennan-specific phenotyping applications. The system’s design and algorithmic architecture are both efficient and adaptable, fully accounting for the morphological characteristics of Phoebe zhennan seedlings and the constraints of nursery data collection while offering the potential for generalization to other morphologically similar species.

From an algorithmic perspective, the method proposed in this study demonstrates clear advantages over both conventional morphological analysis and deep learning-based segmentation approaches. Compared to traditional methods such as the Laplacian operator (Wu et al. [22]), tensor-based approaches (Elnashef et al. [12]), and slicing techniques (Xiang et al. [21]), the proposed algorithm performs multiplanar projection on the initially segmented stem point cloud, followed by a second round of skeleton extraction. This process enhances segmentation accuracy and enables finer identification of stem and leaf structures, thereby compensating for the limitations of traditional methods in structurally complex regions. Compared to current state-of-the-art deep learning methods such as PointNet++ (Qi et al. [17]), PointNeXt (Qian et al. [19]), and PCT (Guo et al. [29]), which, although highly expressive, typically require large amounts of labeled data, high-performance GPUs, and complex training pipelines, making them difficult to deploy in resource-limited environments, the proposed method offers high computational efficiency, low memory consumption, and minimal hardware requirements. These characteristics make it particularly suitable for low-power scenarios, such as edge devices and mobile platforms, while achieving high-precision segmentation without relying on pre-trained models (validated through comparative experiments) and demonstrating enhanced practicality and scalability.

Nevertheless, the algorithm itself exhibits certain limitations, which will serve as focal points for future improvements. On the one hand, when processing the edge regions of Phoebe zhennan stems and leaves, the inherent sparsity in the point cloud distribution may cause the structural features of edge points to be insufficiently distinct, potentially leading to misclassification. This issue becomes particularly prominent in samples exhibiting complex 3D geometries and irregular contours (Wang et al. [30]). A viable solution involves refining the treatment of sparse regions by tuning the parameters of the DBSCAN clustering algorithm, such as decreasing the clustering radius or increasing the minimum point threshold (Gholizadeh et al., [31]). On the other hand, in the transitional region where the stem meets the leaf—particularly near stem nodes—the dense clustering of the point cloud introduces observation bias across different viewpoints, thereby increasing the risk of misclustering. To mitigate this issue, we employed skeleton-based information to differentiate stems and leaves, leveraging their distinct geometric characteristics—cylindrical for stems and curved for leaves—thereby improving segmentation accuracy to a certain degree (Ferrara et al. [32]).

From the perspective of application deployment, extending the system to complex field environments remains challenging(Wang et al. [33]). First, under dense Phoebe zhennan planting conditions, morphological changes induced by stress—such as localized leaf folding and stem bending—are likely to occur. However, the stem length is extracted using the MNVG algorithm, which corrects direction vectors at each point to ensure continuity, thereby allowing the cumulative path length to accurately represent the true stem length—even in the presence of curvature. As a result, stress exerts minimal impact on measurements of stem length and diameter, and only limited influence on parameters such as leaf area; plant height is the most likely to be affected.

Second, in cases where leaves partially occlude stems, a relatively complete 3D reconstruction can still be achieved by increasing multi-angle image capture and performing accurate alignment, thereby maintaining high parameter extraction accuracy (Luo et al. [34]). Although occlusion may affect feature extraction in the locally occluded leaf regions, the impact is limited and does not significantly influence overall phenological measurements. Localized occlusion remains a common challenge that current non-contact phenotyping techniques cannot fully address and often requires inference or manual intervention. In addition, under complex field conditions, more efficient multi-plant segmentation algorithms are required to improve single-plant extraction accuracy, particularly due to severe interleaf overlap among adjacent crops (Liu et al. [35]). Preliminary tests indicate that stem recognition and separation are relatively straightforward, but leaf overlap continues to hinder accurate attribution (Li et al. [36]), representing a primary challenge for future research efforts.

Finally, in terms of cost-effectiveness and generalizability, the system utilizes a low-cost time-of-flight (TOF) camera with a simple hardware configuration that remains both economical and acceptably accurate (Xie et al. [37]). Compared to high-cost solutions like high-precision LiDAR, this system offers greater practicality and cost-efficiency, making it particularly suitable for large-scale deployment in resource-constrained settings, such as seedling nurseries and forestry research stations. By achieving high-precision stem and leaf segmentation with simplified hardware, the system demonstrates strong versatility and scalability across diverse application scenarios.

5. Conclusions

This research developed phenotypic parameter measurement methods for Phoebe zhennan seedlings. Five parameters—stem length, stem diameter, leaf length, leaf width, and leaf area—were extracted from the collected 3D point cloud data in four steps: image preprocessing, point cloud alignment, stem and leaf segmentation, and parameter measurement. The algorithm is primarily based on the concept of median normalized search. Conventional search methods for the same height are less effective due to the structural characteristics of Phoebe zhennan plants, which may produce multiple leaves at the same height. The inhomogeneous distribution of the leaf point cloud and the redundancy in the search radius can lead to search errors, such as failing to extract the stems.

This paper proposes a search correction method that adjusts the search direction of the current point based on the growth direction vectors of the first n growth points. This ensures the correct growth of stem points at the stem-leaf junction and yields better segmentation results. The results demonstrate that the segmentation algorithm effectively extracts each leaf and the main stem from the 3D point cloud of Phoebe zhennan plants. The algorithm for detecting individual leaves and stems was successfully implemented. The system was used to characterize several important parameters of the Phoebe zhennan seedling, yielding promising results. The automatic measurements of the 3D surface model were consistent with the corresponding manual measurements, verifying the accuracy and practicality of the system.

Thus, depth imaging provides an effective and economical solution for plant phenotypic characterization, facilitating genomic research and plant breeding programs. Future work will focus on improving the algorithm to address the leaf occlusion problem. The stem and leaf segmentation scheme will also be refined to improve efficiency and adapt the method to different growing environments and field scenarios.